Curiously "man" is etymologically gender neutral, where wo/wif(man) denoted the female prefix for man, and the male dropped what would otherwise be were(man), seen in for example werewolf, which is gendered.
Yes, "man" is etymologically a person, "woman" is a female person, and "wereman" is a male person. Over time "were" got dropped, but "wo" got kept, so "man" is either a gender-neutral person or a male person, distinguished based on context. E.g. "mankind" is gender-neutral.
“world” is derived from “were” + “eald” (old), and meant “the age of humans”, which was distinguished from the age of the Gods, when the Æsir and Vanir dominated, and the age of the Jötnar.
I find it interesting how the term shifted from a (mythical) temporal concept to a spatial concept, to now often a social concept (e.g. the Fourth World).